Proves that the intersection of maximal analytic Hardy fields coincides with that of all maximal Hardy fields, confirming Boshernitzan's conjecture via relative differential closure.
Normalizing Asymptotic Differential Equations
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abstract
We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization theorems for algebraic differential equations over $H$-fields, as a tool in solving such equations in suitable extensions. The results in this monograph are essential in our work on Hardy fields in [6].
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Relative differential closure in Hardy fields
Proves that the intersection of maximal analytic Hardy fields coincides with that of all maximal Hardy fields, confirming Boshernitzan's conjecture via relative differential closure.